The conventional bicycle is generally provided with a brake system having two brake shoes which are capable of being actuated by the brake cable of the brake system to press against a wheel rim of the bicycle, so as to slow or stop the motion of the bicycle. The bicycle is rather vulnerable to overturn when the brake shoes are so actuated by the brake cable to press against the bicycle wheel rim in a hasty manner to bring the bicycle in motion to an abrupt halt. Needless to say, a bicyclist is therefore vulnerable to injuries when the overturn of the bicycle in motion takes place. Such an overturn incident of the bicycle is especially hazardous when the bicycle is in a downhill motion because of the motion inertia of the bicycle. Under such a downhill circumstance as described above, it is difficult for the bicyclist to manage to keep the rear wheel of the bicycle in a stable condition at such time when the braking action of the front wheel is triggered abruptly by the bicyclist. The solution to such a problem as described above is to apply the brake lever of the bicycle intermittently with skill.